What are the solutions to the equation 2(x^2-2x)^2-5(x^2-2x)=12 ?

The solutions to the equation 2(x^2-2x)^2-5(x^2-2x)=12 are x=-sqrt(5)+1,x=sqrt(5)+1

Find the zeros of 2(x^2-2x)^2-5(x^2-2x)=12

The zeros of 2(x^2-2x)^2-5(x^2-2x)=12 are x=-sqrt(5)+1,x=sqrt(5)+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2 (x^{2} - 2 x)^{2} - 5 (x^{2} - 2 x) = 12

x = - 5 + 1, x = 5 + 1

Decimal Notation

x = - 1.23606 \dots, x = 3.23606 \dots

Solution steps

2 (x^{2} - 2 x)^{2} - 5 (x^{2} - 2 x) = 12

Expand

2 (x^{2} - 2 x)^{2} - 5 (x^{2} - 2 x) : 2 x^{4} - 8 x^{3} + 3 x^{2} + 10 x

2 x^{4} - 8 x^{3} + 3 x^{2} + 10 x = 12

Move

12

to the left side

2 x^{4} - 8 x^{3} + 3 x^{2} + 10 x - 12 = 0

Find one solution for

2 x^{4} - 8 x^{3} + 3 x^{2} + 10 x - 12 = 0

using Newton-Raphson:

x \approx - 1.23606 \dots

Apply long division:

\frac{2 x ^{4} - 8 x ^{3} + 3 x ^{2} + 10 x - 12}{x + 1.23606 \dots} = 2 x^{3} - 10.47213 \dots x^{2} + 15.94427 \dots x - 9.70820 \dots

2 x^{3} - 10.47213 \dots x^{2} + 15.94427 \dots x - 9.70820 \dots \approx 0

Find one solution for

2 x^{3} - 10.47213 \dots x^{2} + 15.94427 \dots x - 9.70820 \dots = 0

using Newton-Raphson:

x \approx 3.23606 \dots

Apply long division:

\frac{2 x ^{3} - 10.47213 \dots x ^{2} + 15.94427 \dots x - 9.70820 \dots}{x - 3.23606 \dots} = 2 x^{2} - 4 x + 3

2 x^{2} - 4 x + 3 \approx 0

Find one solution for

2 x^{2} - 4 x + 3 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx - 1.23606 \dots : x = - 5 + 1

x \approx 3.23606 \dots : x = 5 + 1

x = - 5 + 1, x = 5 + 1

The solutions are

x = - 5 + 1, x = 5 + 1

x^{4} - 5 x^{2} - 50 = 0

t = - 3.9 (t)^{2} - (t)^{4}

x, y = q^{2} + (a x)^{3}

x^{4} = 24 x + 32

12 (k^{3} - 4 k^{2} + k + 6) = 0

What are the solutions to the equation 2(x^2-2x)^2-5(x^2-2x)=12 ?
The solutions to the equation 2(x^2-2x)^2-5(x^2-2x)=12 are x=-sqrt(5)+1,x=sqrt(5)+1
Find the zeros of 2(x^2-2x)^2-5(x^2-2x)=12
The zeros of 2(x^2-2x)^2-5(x^2-2x)=12 are x=-sqrt(5)+1,x=sqrt(5)+1